mektek iv

SOAL

DIKETAHUI :- P = 18.8 t- q = 18.8 t/m- EI Balok = 1- EI Kolom = 2- a = 7 m- b = 3 m- c = 5 m- d = 5 m- LV = 4 m- LH = 10 m

==

5 5 5 5

7 3 7 3

4

4

PP

P P

q

q

A B C

D E F

G H I

PENYELESAIAN

A. MENENTUKAN FAKTOR DISTRIBUSI MASING - MASING BENTANG

² Titik D

-» kDA =4EI

=4 2 E I

= 2.00000 EIL 4

-» kDE =4EI

=4 1 E I

= 0.40000 EIL 10

-» kDG =4EI

=4 2 E I

= 2.00000 EIL 4

² Titik E

-» kED =4EI

=4 1 E I

= 0.40000 EIL 10

-» kEH =4EI

=4 2 E I

= 2.00000 EIL 4

-» kEF =4EI

=4 1 E I

= 0.40000 EIL 10

-» kEB =4EI

=4 2 E I

= 2.00000 EIL 4

² Titik F

-» kFE =4EI

=4 1 E I

= 0.40000 EIL 10

-» kFI =4EI

=4 2 E I

= 2.00000 EIL 4

-» kFC =4EI

=4 2 E I

= 2.00000 EIL 4

² Titik G

-» kGD =4EI

=4 2 E I

= 2.00000 EIL 4

-» kGH =4EI

=4 1 E I

= 0.40000 EIL 10

² Titik H

-» kHG =4EI

=4 1 E I

= 0.40000 EIL 10

-» kHE =4EI

=4 2 E I

= 2.00000 EIl 4

-» kHI =4EI

=4 1 E I

= 0.40000 EIL 10

² Titik I-» kIF = 4EI

=4 2 E I

= 2.00000 EIL 4

-» kIH = 4EI=

4 1 E I= 0.40000 EI

L 10

B. PERHITUNGAN KOEFISIEN DISTRIBUSI ( µ )

² Titik D

-» µ DA =kDA

=2.00000

= 0.45455∑kD 4.40000

-» µ DE =kDE

=0.40000

= 0.09091 ∑µD = 1.00000∑kD 4.40000

-» µ DG =kDG

=2.00000

= 0.45455∑kD 4.40000

² Titik E

-» µ ED =kED

=0.40000

= 0.08333∑kE 4.80000

-» µ EH =kEH

=2.00000

= 0.41667∑kE 4.80000

∑µE = 1.00000

-» µ EF =kEF

=0.40000

= 0.08333∑µE = 1.00000

∑kE 4.80000

-» µ EB =kEB

=2.00000

= 0.41667∑kE 4.80000

² Titik F

-» µ FE =kFE = 0.40000

= 0.09091∑kF 4.40000

∑µF = 1.00000-» µ FI =

kFI=

2.00000= 0.45455

∑kF 4.40000

-» µ FC =kFC = 2.00000

= 0.45455∑kF 4.40000

² Titik G

-» µ GD =kGD

=2.00000

= 0.83333∑kG 2.40000

∑µG = 1.00000-» µ GH =

kGA=

0.40000= 0.16667

∑kG 2.40000² Titik H

-» µ HG =kHG

=0.40000

= 0.14286∑kG 2.80000

-» µ HE =kHE

=2.00000

= 0.71429 ∑µH = 1.00000∑kG 2.80000

-» µ HI =kHI 0.40000

= 0.14286∑kG 2.80000

² Titik I

-» µ IF= kIF = 2.00000

= 0.83333∑kI 2.40000

∑µI = 1.00000-» µ IH

= kIH = 0.40000= 0.16667

∑kI 2.40000

C.²

- BATANG DE

= (1

. q ) +12

= (1

. 18.800 10 2 ) +18.800 7 3 2

12 10 2

= 156.66667 + 11.84400

= 168.51067 tm

= ( -1

. q ) -12

= ( -1

. 18.800 10 2 ) -18.800 7 2 3

12 10 2

= -156.66667 - 27.63600

= -184.30267 tm

PERHITUNGAN MOMEN PRIMER ( M0 )PERHITUNGAN M0 AKIBAT BEBAN LUAR

M0DE L2P. a . b2

L2

M0ED L2P. a2.b

L2

D E

q

7 3

P

- BATANG GH

= (1

. q ) +12

= (1

. 18.800 10 2 ) +18.800 5 5 2

12 10 2

= 156.66667 + 23.50000

= 180.16667 tm

= ( -1

. q ) -12

= ( -1

. 18.800 10 2 ) -18.800 5 2 5

12 10 2

= -156.66667 - 23.50000

= -180.16667 tm

KETERANGAN

- = DE = 168.51067 tm- = EF = 168.51067 tm- = ED = -184.30267 tm- = FE = -184.30267 tm- = GH = 180.16667 tm- = HI = 180.16667 tm- = HG = -180.16667 tm- = IH = -180.16667 tm

M0GH L2P. c . d2

L2

M0HG L2P. c2.d

L2

M0

M0

M0

M0

M0

M0

M0

M0

G H

q

5

P

5

ITERASI MOMEN AKIBAT BEBAN LUAR

Titik C B A D G H I F E

Batang CF BE AD DA DE DG GD GH HG HE HI IH IF FI FC FE EF EH ED EB

µ -0.45455 -0.09091 -0.45455 -0.83333 -0.16667 -0.14286 -0.71429 -0.14286 -0.16667 -0.83333 -0.45455 -0.45455 -0.09091 -0.08333 -0.41667 -0.08333 -0.41667

168.51067 180.16667 -180.16667 180.16667 -180.16667 -184.30267 168.51067 -184.30267

24.90570 2.96836 -38.29788 -76.59576 -15.31915 -76.59576 -38.29788

0.59367 -59.11199 -118.22399 -23.64480 -11.82240

2.11038 0.60295 13.29962 26.59924 5.31985 26.59924 13.29962 0.84446 1.68891 8.44457 1.68891 0.84446

0.12059 -5.89336 -11.78673 -2.35735 -1.17867 2.96836 14.94352 29.88703 149.43517 74.71759

0.18179 -0.16512 1.31199 2.62399 0.52480 2.62399 1.31199 -1.19523 -2.39046 -11.95229 -2.39046 -1.19523 24.90570 49.81140 49.81140 9.96228 4.98114 4.22229 -7.65958

-0.03302 -0.04865 -0.09730 -0.01946 -0.00973 0.60295 -1.97587 -3.95175 -19.75873 -9.87936 0.59367 1.18735 5.93673 1.18735 5.93673

0.02715 -0.02862 0.01856 0.03713 0.00743 0.03713 0.01856 0.09876 0.19752 0.98761 0.19752 0.09876 2.11038 4.22077 4.22077 0.84415 0.42208 -5.97615 2.65992

-0.00572 -0.04888 -0.09777 -0.01955 -0.00978 -0.16512 -0.18410 -0.36819 -1.84095 -0.92048 0.12059 0.24118 1.20589 0.24118 1.20589

0.00420 -0.00434 0.01241 0.02482 0.00496 0.02482 0.01241 0.02564 0.05128 0.25642 0.05128 0.02564 0.18179 0.36359 0.36359 0.07272 0.03636 0.49381 0.26240

-0.00087 -0.01586 -0.03171 -0.00634 -0.00317 -0.02862 -0.01729 -0.03457 -0.17286 -0.08643 -0.03302 -0.06605 -0.33023 -0.06605 -0.33023

0.00065 -0.00074 0.00380 0.00760 0.00152 0.00760 0.00380 0.00351 0.00701 0.03505 0.00701 0.00351 0.02715 0.05430 0.05430 0.01086 0.00543 0.12821 0.00371

-0.00015 -0.00304 -0.00609 -0.00122 -0.00061 -0.00434 -0.00255 -0.00511 -0.02554 -0.01277 -0.00572 -0.01145 -0.05723 -0.01145 -0.05723

0.00010 -0.00013 0.00073 0.00145 0.00029 0.00145 0.00073 0.00054 0.00107 0.00536 0.00107 0.00054 0.00420 0.00841 0.00841 0.00168 0.00084 0.01753 0.00248

-0.00003 -0.00053 -0.00105 -0.00021 -0.00011 -0.00074 -0.00039 -0.00079 -0.00395 -0.00197 -0.00087 -0.00174 -0.00869 -0.00174 -0.00869

0.00002 -0.00002 0.00013 0.00025 0.00005 0.00025 0.00013 0.00009 0.00018 0.00089 0.00018 0.00009 0.00065 0.00129 0.00129 0.00026 0.00013 0.00268 0.00076

0.00000 -0.00009 -0.00018 -0.00004 -0.00002 -0.00013 -0.00006 -0.00012 -0.00061 -0.00031 -0.00015 -0.00030 -0.00149 -0.00030 -0.00149

0.00000 0.00000 0.00002 0.00004 0.00001 0.00004 0.00002 0.00001 0.00003 0.00015 0.00003 0.00001 0.00010 0.00021 0.00021 0.00004 0.00002 0.00044 0.00015

0.00000 -0.00001 -0.00003 -0.00001 0.00000 -0.00002 -0.00001 -0.00002 -0.00010 -0.00005 -0.00003 -0.00005 -0.00025 -0.00005 -0.00025

0.00000 0.00000 0.00000 0.00001 0.00000 0.00001 0.00000 0.00000 0.00000 0.00002 0.00000 0.00000 0.00002 0.00003 0.00003 0.00001 0.00000 0.00007 0.00003

0.00000 0.00000 -0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00002 -0.00001 0.00000 -0.00001 -0.00004 -0.00001 -0.00004

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00001 0.00001 0.00000 0.00000 0.00001 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00001 0.00000 -0.00001

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000

27.23000 3.37234 -23.65061 -47.30123 159.72489 -112.42366 -153.89547 153.89547 -193.63559 1.15013 192.48547 -154.86241 154.86241 118.27620 54.46000 -172.73620 175.30560 5.63357 -187.68385 6.74468

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

OK !!! OK !!! OK !!! OK !!! OK !!! OK !!!

M0

²

LANTAI 1-

=6 EI

=6 2 EI4 2

- AD = 0.75000 tm- BE = 0.75000 tm- CF = 0.75000 tm- FC = 0.75000 tm- EB = 0.75000 tm- DA = 0.75000 tm

LANTAI 2- = -6 EI

= -6 2 EI4 2

- DG = -0.75000 tm- EH = -0.75000 tm- FI = -0.75000 tm- IF = -0.75000 tm- HE = -0.75000 tm- GD = -0.75000 tm

PERHITUNGAN M 0 AKIBAT PERGOYANGAN I

M0

L2

M0

M0

M0

M0

M0

M0

M0

L2

M0

M0

M0

M0

M0

M0

A B C

D E F

G H IEI

2 EI

EI

EI

EI

2 EI 2 EI

2 EI 2 EI 2 EI

ITERASI MOMEN AKIBAT PERGOYANGAN I



µ -0.45455 -0.09091 -0.45455 -0.83333 -0.16667 -0.14286 -0.71429 -0.14286 -0.16667 -0.83333 -0.45455 -0.45455 -0.09091 -0.08333 -0.41667 -0.08333 -0.41667

0.75000 0.75000 0.75000 0.75000 -0.75000 -0.75000 -0.75000 -0.75000 -0.75000 0.75000 -0.75000 0.75000

-0.06637 -0.04839 0.00000 0.00000 0.00000 0.00000 0.00000

-0.00968 0.31250 0.62500 0.12500 0.06250

-0.00416 0.00391 -0.06882 -0.13765 -0.02753 -0.13765 -0.06882 0.04911 0.09821 0.49107 0.09821 0.04911

0.00078 0.00822 0.01643 0.00329 0.00164 -0.04839 0.05841 0.11682 0.58408 0.29204

-0.00064 0.00084 -0.00204 -0.00409 -0.00082 -0.00409 -0.00204 -0.00083 -0.00167 -0.00833 -0.00167 -0.00083 -0.06637 -0.13274 -0.13274 -0.02655 -0.01327 0.24554 0.00000

0.00017 0.00120 0.00240 0.00048 0.00024 0.00391 0.00560 0.01120 0.05600 0.02800 -0.00968 -0.01936 -0.09678 -0.01936 -0.09678

-0.00011 0.00012 -0.00031 -0.00062 -0.00012 -0.00062 -0.00031 -0.00070 -0.00139 -0.00696 -0.00139 -0.00070 -0.00416 -0.00833 -0.00833 -0.00167 -0.00083 -0.00417 -0.01376

0.00002 0.00042 0.00084 0.00017 0.00008 0.00084 0.00041 0.00081 0.00405 0.00203 0.00078 0.00156 0.00782 0.00156 0.00782

-0.00002 0.00002 -0.00010 -0.00020 -0.00004 -0.00020 -0.00010 -0.00009 -0.00019 -0.00095 -0.00019 -0.00009 -0.00064 -0.00128 -0.00128 -0.00026 -0.00013 -0.00348 -0.00041

0.00000 0.00008 0.00016 0.00003 0.00002 0.00012 0.00006 0.00012 0.00061 0.00031 0.00017 0.00033 0.00167 0.00033 0.00167

0.00000 0.00000 -0.00002 -0.00004 -0.00001 -0.00004 -0.00002 -0.00001 -0.00003 -0.00014 -0.00003 -0.00001 -0.00011 -0.00021 -0.00021 -0.00004 -0.00002 -0.00047 -0.00006

0.00000 0.00001 0.00003 0.00001 0.00000 0.00002 0.00001 0.00002 0.00010 0.00005 0.00002 0.00005 0.00023 0.00005 0.00023

0.00000 0.00000 0.00000 -0.00001 0.00000 -0.00001 0.00000 0.00000 0.00000 -0.00002 0.00000 0.00000 -0.00002 -0.00003 -0.00003 -0.00001 0.00000 -0.00007 -0.00002

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00002 0.00001 0.00000 0.00001 0.00004 0.00001 0.00004

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00001 -0.00001 0.00000 0.00000 -0.00001 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00001 0.00000 0.00001

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000

0.67870 0.70650 0.67870 0.60740 -0.03722 -0.57017 -0.17644 0.17644 0.15942 -0.31884 0.15942 0.17644 -0.17644 -0.57017 0.60740 -0.03722 -0.03166 -0.59967 -0.03166 0.66300

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

OK !!! OK !!! OK !!! OK !!! OK !!! OK !!!

M0

²

- = 6 EI

= 6 2 EI4 2

- DG = 0.75000 tm- EH = 0.75000 tm- FI = 0.75000 tm- IF = 0.75000 tm- HE = 0.75000 tm- GD = 0.75000 tm

PERHITUNGAN M 0 AKIBAT PERGOYANGAN II

M0

L2

M0

M0

M0

M0

M0

M0

D E F

G H IEI

2 EI

EI

EI

EI

2 EI 2 EI

2 EI 2 EI 2 EI

A B C

ITERASI MOMEN AKIBAT PERGOYANGAN II



µ -0.45455 -0.09091 -0.45455 -0.83333 -0.16667 -0.14286 -0.71429 -0.14286 -0.16667 -0.83333 -0.45455 -0.45455 -0.09091 -0.08333 -0.41667 -0.08333 -0.41667

0.75000 0.75000 0.75000 0.75000 0.75000 0.75000

-0.10418 -0.09260 -0.17045 -0.34091 -0.06818 -0.34091 -0.17045

-0.01852 -0.24148 -0.48295 -0.09659 -0.04830

-0.00463 -0.01355 0.05909 0.11818 0.02364 0.11818 0.05909 -0.05012 -0.10024 -0.50122 -0.10024 -0.05012

-0.00271 -0.00374 -0.00747 -0.00149 -0.00075 -0.09260 -0.05832 -0.11665 -0.58323 -0.29162

0.00022 -0.00058 0.00147 0.00293 0.00059 0.00293 0.00147 0.01083 0.02167 0.10833 0.02167 0.01083 -0.10418 -0.20836 -0.20836 -0.04167 -0.02084 -0.25061 -0.03409

-0.00012 -0.00512 -0.01025 -0.00205 -0.00102 -0.01355 0.00778 0.01556 0.07779 0.03889 -0.01852 -0.03704 -0.18519 -0.03704 -0.18519

0.00005 -0.00008 0.00119 0.00238 0.00048 0.00238 0.00119 0.00049 0.00097 0.00486 0.00097 0.00049 -0.00463 -0.00926 -0.00926 -0.00185 -0.00093 0.05417 0.01182

-0.00002 -0.00070 -0.00140 -0.00028 -0.00014 -0.00058 0.00035 0.00069 0.00345 0.00173 -0.00271 -0.00542 -0.02711 -0.00542 -0.02711

0.00001 -0.00002 0.00016 0.00032 0.00006 0.00032 0.00016 0.00003 0.00005 0.00026 0.00005 0.00003 0.00022 0.00045 0.00045 0.00009 0.00004 0.00243 0.00029

0.00000 -0.00008 -0.00016 -0.00003 -0.00002 -0.00008 -0.00002 -0.00004 -0.00021 -0.00010 -0.00012 -0.00023 -0.00115 -0.00023 -0.00115

0.00000 0.00000 0.00002 0.00004 0.00001 0.00004 0.00002 0.00001 0.00002 0.00008 0.00002 0.00001 0.00005 0.00010 0.00010 0.00002 0.00001 0.00013 0.00024

0.00000 -0.00001 -0.00002 0.00000 0.00000 -0.00002 0.00000 -0.00001 -0.00005 -0.00002 -0.00002 -0.00003 -0.00016 -0.00003 -0.00016

0.00000 0.00000 0.00000 0.00001 0.00000 0.00001 0.00000 0.00000 0.00000 0.00002 0.00000 0.00000 0.00001 0.00002 0.00002 0.00000 0.00000 0.00004 0.00003

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00001 0.00000 0.00000 -0.00001 -0.00003 -0.00001 -0.00003

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00001 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00001 0.00000 -0.00001

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000

-0.10852 -0.10683 -0.10852 -0.21705 -0.06477 0.28182 0.13922 -0.13922 -0.12776 0.25551 -0.12776 -0.13922 0.13922 0.28182 -0.21705 -0.06477 -0.06443 0.34252 -0.06443 -0.21365

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

OK !!! OK !!! OK !!! OK !!! OK !!! OK !!!

M0

D. MENGHITUNG GAYA HORISONTAL

² LANTAI 1

- AKIBAT BEBAN LUAR

H°I =M AD + M DA + M BE + M EB + M CF + M FC

L

H°I =-23.65061 + -47.30123 + 3.37234 + 6.74468 + 27.23000 + 54.46000

4.00000

=20.855174.00000

= 5.21379

- AKIBAT PERGOYANGAN 1


L

H°I =0.67870 + 0.60740 + 0.70650 + 0.66300 + 0.67870 + 0.60740

4.00000

=3.941684.00000

= 0.98542



L

H°I =-0.10852 + -0.21705 + -0.10683 + -0.21365 + -0.10852 + -0.21705

4.00000

=-0.971624.00000

= -0.24291

² LANTAI 2- AKIBAT BEBAN LUAR

H°I =M DG + M GD + M EH + M HE + M FI + M IF

L

H°I =-112.42366 + -153.89547 + 5.63357 + 1.15013 + 118.27620 + 154.86241

4.00000

=13.603184.00000

= 3.40079



L

H°I =-0.57017 + -0.17644 + -0.59967 + -0.31884 + -0.57017 + -0.17644

4.00000

=-2.411734.00000

= -0.60293



L

H°I =0.28182 + 0.13922 + 0.34252 + 0.25551 + 0.28182 + 0.13922

4.00000

=1.440124.00000

= 0.36003

² PERSAMAAN GARIS HORIZONTAL

5.21379 + 0.98542 x + -0.24291 y = 0.000003.40079 + -0.60293 x + 0.36003 y = 0.00000

5.21379 + 0.98542 x + -0.24291 y = 0.00000 x 1.00000-2.29446 + 0.40679 x + -0.24291 y = 0.00000 - x -0.67468

7.50825 + 0.57863 x + 0.00000 y = 0.000000.57863 x = -7.50825

x = -12.97589Disubstitusikan ke persamaan I

5.21379 + ( 0.98542 . x ) + -0.24291 y = 0.000005.21379 + ( 0.98542 . -12.97589 ) + -0.24291 y = 0.000005.21379 + ( -12.78670 ) + -0.24291 y = 0.00000

-7.57291 + -0.24291 y = 0.00000-0.24291 y = 7.57291

y = -31.17638

M = B.Luar +(pergoyangan I.(X))+(pergoyangan II.(Y))

TITIK BTGMOMEN

X Y M Σ MB. LUAR PERG.1 PERG.2

C CF 27.23000 0.67870 -0.10852

-12.97589 -31.17638

21.80668 21.80668B BE 3.37234 0.70650 -0.10683 -2.46468 -2.46468A AD -23.65061 0.67870 -0.10852 -29.07392 -29.07392

DDA -47.30123 0.60740 -0.21705 -48.41593

0.00003DE 159.72489 -0.03722 -0.06477 162.22731DG -112.42366 -0.57017 0.28182 -113.81135

GGD -153.89547 -0.17644 0.13922 -155.94632

0.00000GH 153.89547 0.17644 -0.13922 155.94632

HHG -193.63559 0.15942 -0.12776 -191.72118

0.00001HE 1.15013 -0.31884 0.25551 -2.67870HI 192.48547 0.15942 -0.12776 194.39988

IIH -154.86241 0.17644 -0.13922 -152.81156

0.00000IF 154.86241 -0.17644 0.13922 152.81156

FFI 118.27620 -0.57017 0.28182 116.88850

0.00000FC 54.46000 0.60740 -0.21705 53.34528FE -172.73620 -0.03722 -0.06477 -170.23378

E

EF 175.30560 -0.03166 -0.06443 177.72528

0.00000EH 5.63357 -0.59967 0.34252 2.73633ED -187.68385 -0.03166 -0.06443 -185.26417EB 6.74468 0.66300 -0.21365 4.80256

² KONTROL H

LANTAI 1


L

H°I =-29.07392 + -48.41593 + -2.46468 + 4.80256 + 21.80668 + 53.34528

4.00000

=0.000004.00000

= 0.00000

LANTAI 2

H°II =M DG + M GD + M EH + M HE + M FI + M IF

L

H°II =-113.81135 + -155.94632 + 2.73633 + -2.67870 + 116.88850 + 152.81156

4.00000

=0.000004.00000

= 0.00000

D. PERHITUNGAN MOMEN ( M ) DAN GAYA LINTANG ( D )

² BATANG DE

162.22731 18.8 185.26417

18.8

7 3

» Reaksi

∑ ME = 0

RDE .

RDE . 10 - 162.22731 - ( 18.8 . 3 ) - ( 0.5 . 18.8 . 10 2 ) + 185.26417 = 0.00000

10 RDE - 162.22731 - 56.4 - 940.0 + 185.3 = 0.00000

10 RDE -973.36314 = 0.00000

RDE = 97.33631 ton …..↑∑ MD = 0

-RED .

-RED . 10 + 185.26417 + ( 18.8 . 7 ) + ( 0.5 . 18.8 . 10 2 ) - 162.22731 = 0.00000

-10 RED + 185.26417 + 131.6 + 940.0 - 162.22731 = 0.00000

-10 RED + 1094.63686 = 0.00000

RED = 109.46369 ton …..↑» Bidang M dan D

Interval : ( 0 ≤ X ≤ 7 )

Mx =

= 97.33631 . X - 0.5 18.8 . X² -162.22731

= -9.40000 . X² + 97.33631 .X -162.22731

X 0 1 2 3 4 5 6 7

Mx -162.22731 -74.29100 -5.15468 45.18163 76.71794 89.45426 83.39057 58.52689

Letak M = 0 pada interval ( 0 ≤ X ≤ 7 )

Mx = -9.40000 . X² + 97.33631 .X -162.22731

a = -9.40000

b = 97.33631

c = -162.22731

X =-b ± b² - 4ac

2a

X =-97.33631 ± 97.33631 2 - 4 -9.40000 . -162.22731

2 -9.40000

X =-97.33631 ± 58.09140

-18.80000

=-97.33631 + 58.09140

-18.80000

= 2.087495

=-97.33631 -58.09140

-18.80000

= 8.26743

L - MDE - (P.l ) - (1/2 . q . L2 )+ MED = 0

L + MED +( P.l ) + ( 1/2 . q . L2 ) - MDE = 0

RDE . X - 1/2.q.X2 - MDE

X1

X2

1/2

1/2

D E

Mx = 0

M ( 2.087495 ) = -9.40000 .( 2.08750 2 )+( 97.33631 2.08750 ) -162.22731

= 0.00000 …..OK!!!!

Mmax = -9.40000 . X² + 97.33631 .X -162.22731

dmx= -18.80000 X+ 97.33631

dx

X =97.33631

18.80000

= 5.17746

Mmax = ( -9.40000 . 5.17746 2 )+( 97.33631 5.17746 ) -162.22731

= 89.75030 tm

Dx = RDE - ( q . X )

= 97.33631 - ( 18.8000 X )

X 0 1 2 3 4 5 6 7

Dx 97.33631 78.53631 59.73631 40.93631 22.13631 3.33631 -15.46369 -34.26369

Interval : ( 7 ≤ X ≤ 10 )

Mx =

= 97.33631 . X - 0.5 18.8 . X² - 162.22731 - 18.80000 ( X - 7 )

= 97.33631 . X - 0.5 18.8 . X² - 162.22731 - 18.80000 X + 131.60000

= -9.40000 . X² + 78.53631 . X -30.62731

X 7 8 9 10

Mx 58.52689 -3.93680 -85.20049 -185.26417


Mx = -9.40000 . X² + 78.53631 .X -30.62731

a = -9.40000

b = 78.53631

c = -30.62731

X =-b ± b² - 4ac

2a

X =-78.53631 ± 78.53631 2 - 4 -9.40000 . -30.62731

2 -9.40000

X =-78.53631 ± 70.82631

-18.80000

=-78.53631 + 70.82631

-18.80000

= 0.41011

=-78.53631 -70.82631

-18.80000

= 7.94482

RDE . X - 1/2.q . X2 - MDE - P ( x-7 )

X1

X2

Mx = 0

M ( 0.41011 ) = -9.40000 .( 0.41011 2 )+( 78.53631 0.41011 ) -30.62731

= 0.00000 …..OK!!!!

Mmax = -9.40000 . X² + 78.53631 .X -30.62731

dmx= -18.80000 X+ 78.53631

dx

X =78.53631

18.80000

= 4.17746 …..( tidak ada nilai maksimum )

Dx = RDE - ( q.X ) - P

= 97.33631 - ( 18.80000 . X ) - 18.80000

= 78.53631 - ( 18.80000 . X )

X 7 8 9 10

Dx -53.06369 -71.86369 -90.66369 -109.46369

² BATANG EF

177.72528 18.8 170.23378

18.8

7 3

» Reaksi

∑ MF = 0

REF .

REF . 10 - 177.72528 - ( 18.8 . 3 ) - ( 0.5 . 18.8 . 10 2 ) + 170.23378 = 0.00000

10 REF - 177.72528 - 56.4 - 940.0 + 170.23378 = 0.00000

10 REF -1003.89150 = 0.00000

REF = 100.38915 ton …..↑∑ ME = 0

-RFE .

-RFE . 10 + 170.23378 + ( 18.8 . 7 ) + ( 0.5 . 18.8 . 10 2 ) - 177.72528 = 0.00000

-10 RFE + 170.23378 + 131.6 + 940.0 - 177.72528 = 0.00000

-10 RFE + 1064.10850 = 0.00000

RFE = 106.41085 ton …..↑» Bidang M dan D

Interval : ( 0 ≤ X ≤ 7 )

Mx =

= 100.389150 . X - 0.5 18.8 . X² -177.72528

= -9.40000 . X² + 100.38915 .X -177.72528

X 0 1 2 3 4 5 6 7

Mx -177.72528 -86.73613 -14.54698 38.84217 73.43132 89.22047 86.20962 64.39877

L - MEF - P.l - 1/2 . q . L2 + MFE = 0

L + MFE + P.l + 1/2 . q . L2 - MEF = 0

REF X - 1/2.q.X2 - MEF

1/2

1/2

E F


Mx = -9.40000 . X² + 100.38915 .X -177.72528

a = -9.40000

b = 100.38915

c = -177.72528

X =-b ± b² - 4ac

2a

X =-100.38915 ± 100.38915 2 - 4 -9.40000 . -177.72528

2 -9.40000

X =-100.38915 ± 58.27101

-18.80000

=-100.38915 + 58.27101

-18.80000

= 2.24033

=-100.38915 -58.27101

-18.80000

= 8.43937

Mx = 0

M ( 2.24033 ) = -9.40000 .( 2.24033 2 )+( 100.38915 2.24033 ) -177.72528

= 0.00000 …..OK!!!!

Mmax = -9.40000 . X² + 100.38915 .X -177.72528

dmx= -18.80000 X+ 100.38915

dx

X =100.38915

18.80000

= 5.33985

Mmax = -9.40000 .( 5.33985 2 )+( 100.38915 5.33985 ) -177.72528

= 90.30614 tm

Dx = REF - ( q.X )

= 100.3892 - ( 18.8000 X )

X 0 1 2 3 4 5 6 7

Dx 100.38915 81.58915 62.78915 43.98915 25.18915 6.38915 -12.41085 -31.21085

Interval : ( 7 ≤ X ≤ 10 )

Mx =

= 100.38915 . X - 0.5 18.8 . X² - 177.72528 - 18.80000 X + 131.60000

= -9.40000 . X² + 81.58915 . X -46.12528

X 7 8 9 10

Mx 64.39877 4.98792 -73.22293 -170.23378

X1

X2

REF.X - 1/2.q.X2 - MEF - P ( x-7 )

Letak M=0 pada interval ( 7 ≤ X ≤ 10 )

Mx = -9.40000 . X² + 81.58915 .X -46.12528

a = -9.40000

b = 81.58915

c = -46.12528

X =-b ± b² - 4ac

2a

X =-81.58915 ± 81.58915 2 - 4 -9.40000 . -46.12528

2 -9.40000

X =-81.58915 ± 70.16038

-18.80000

=-81.58915 + 70.16038

-18.80000

= 0.60791

=-81.58915 -70.16038

-18.80000

= 8.07178

Mx = 0

M ( 0.60791 ) = -9.40000 .( 0.60791 2 )+( 81.58915 0.60791 ) -46.12528

= 0.00000 …..OK!!!!

Mmax = -9.40000 . X² + 81.58915 .X -46.12528

dmx= -18.80000 X+ 81.58915

dx

X =81.58915

18.80000


Dx = REF - ( q.X ) - P

= 100.38915 - ( 18.80000 X ) - 18.80000

= 81.58915 - ( 18.80000 X )

X 7 8 9 10

Dx -50.01085 -68.81085 -87.61085 -106.41085

² BATANG GH

155.94632 18.8 191.72118

18.8

G H

5 5

» Reaksi

∑ MH = 0

X1

X2

RGH .

RGH . 10 - 155.94632 - ( 18.8 . 5 ) - ( 0.5 . 18.8 . 10 2 ) + 191.72118 = 0.00000

10 RGH - 155.94632 - 94.0 - 940.0 + 191.72118 = 0.00000

10 RGH -998.22514 = 0.00000

RGH = 99.82251 ton …..↑

∑ MG = 0

-RHG .

-RHG . 10 + 191.72118 + ( 18.8 . 5 ) + ( 0.5 . 18.8 . 10 2 ) - 155.94632 = 0.00000

-10 RHG + 191.72118 + 94.0 + 940.0 - 155.94632 = 0.00000

-10 RHG + 1069.77486 = 0.00000

RHG = 106.97749 ton …..↑» Bidang M dan D

Interval : ( 0 ≤ X ≤ 5 )

Mx =

= 99.82251 . X - 0.5 18.8 . X² -155.94632

= -9.40000 . X² + 99.82251 .X -155.94632

X 0 1 2 3 4 5

Mx -155.94632 -65.52381 6.09871 58.92122 92.94374 108.16625


Mx = -9.40000 . X² + 99.82251 .X -155.94632

a = -9.40000

b = 99.82251

c = -155.94632

X =-b ± b² - 4ac

2a

X =-99.82251 ± 99.82251 2 - 4 -9.40000 . -155.94632

2 -9.40000

X =-99.82251 ± 64.03868

-18.80000

=-99.82251 + 64.03868

-18.80000

= 1.90340

=-99.82251 -64.03868

-18.80000

= 8.71602

Mx = 0

M ( 1.90340 ) = -9.40000 .( 1.90340 2 )+( 99.82251 1.90340 ) -155.94632

= 0.00000 …..OK!!!!

Mmax = -9.40000 . X² + 99.82251 .X -155.94632

dmx= -18.80000 X+ 99.82251

dx

L - MGH - P.l - 1/2 . q . L2 + MHG = 0

L + MHG + P.l + 1/2 . q . L2 - MGH = 0

RGH.X - 1/2.q.X2 - MGH

X1

X2

1/2

1/2

X =99.82251

18.80000


Dx = RGH - ( q.X )

= 99.82251 - ( 18.80000 . X )

X 0 1 2 3 4 5

Dx 99.82251 81.02251 62.22251 43.42251 24.62251 5.82251

Interval : ( 5 ≤ X ≤ 10 )

Mx =

= 99.82251 . X - 0.5 18.8 . X² - 155.94632 - 18.80000 X + 94.00000

= -9.40000 . X² + 81.02251 . X -61.94632

X 5 6 7 8 9 10

Mx 108.16625 85.78877 44.61128 -15.36621 -94.14369 -191.72118


Mx = -9.40000 . X² + 81.02251 .X -61.94632

a = -9.40000

b = 81.02251

c = -61.94632

X =-b ± b² - 4ac

2a

X =-81.02251 ± 81.02251 2 - 4 -9.40000 . -61.94632

2 -9.40000

X =-81.02251 ± 65.08046

-18.80000

=-81.02251 + 65.08046

-18.80000

= 0.84798

=-81.02251 -65.08046

-18.80000

= 7.77143

Mx = 0

M ( 0.84798 ) = -9.40000 .( 0.84798 2 )+( 81.02251 0.84798 ) -61.94632

= 0.00000 …..OK!!!!

Mmax = -9.40000 . X² + 81.02251 .X -61.94632

dmx= -18.80000 X+ 81.02251

dx

X =81.02251

18.80000

= 4.30971

Mmax = -9.40000 .( 4.30971 2 )+( 81.02251 4.30971 ) -61.94632

RGH.X - 1/2.q.X2 - MGH - P ( x-5 )

X1

X2

= 112.64538 tm

Dx = RGH - ( q.X ) - P

= 99.82251 - ( 18.80000 . X ) - 18.80000

= 81.02251 - ( 18.80000 . X )

X 5 6 7 8 9 10

Dx -12.97749 -31.77749 -50.57749 -69.37749 -88.17749 -106.97749

² BATANG HI

194.39988 18.8 152.81156

18.8

H I

5 5

» Reaksi

∑ MI = 0

RHI .

RHI . 10 - 194.39988 - ( 18.8 . 5 ) - ( 0.5 . 18.8 . 10 2 ) + 152.81156 = 0.00000

10 RHI - 194.39988 - 94.0 - 940.00 + 152.81156 = 0.00000

10 RHI -1075.58832 = 0.00000

RHI = 107.55883 ton …..↑∑ MH = 0

-RIH .

-RIH . 10 + 152.81156 + ( 18.8 . 5 ) + ( 0.5 . 18.8 . 10 2 ) - 194.39988 = 0.00000

-10 RIH + 152.81156 + 94.0 + 940.0 - 194.39988 = 0.00000

-10 RIH + 992.41168 = 0.00000

RIH = 99.24117 ton …..↑» Bidang M dan D

Interval : ( 0 ≤ X ≤ 5 )

Mx =

= 107.55883 . X - 0.5 18.8 . X² -194.39988

= -9.40000 . X² + 107.55883 .X -194.39988

X 0 1 2 3 4 5

Mx -194.39988 -96.24105 -16.88222 43.67661 85.43545 108.39428


Mx = -9.40000 . X² + 107.55883 .X -194.39988

a = -9.40000

b = 107.55883

c = -194.39988

X =-b ± b² - 4ac

2a

X =-107.55883 ± 107.55883 2 - 4 -9.40000 . -194.39988

2 -9.40000

L - MHI - P.l - 1/2 . q . L2 + MIH = 0

L + MIH + P.l + 1/2 . q . L2 - MHI = 0

RHI.X - 1/2.q.X2 - MHI

1/2

1/2

X =-107.55883 ± 65.26459

-18.80000

=-107.55883 + 65.26459

-18.80000

= 2.24969

=-107.55883 -65.26459

-18.80000

= 9.19274

Mx = 0

M ( 2.24969 ) = -9.40000 .( 2.24969 2 )+( 107.55883 2.24969 ) -194.39988

= 0.00000 …..OK!!!!

Mmax = -9.40000 . X² + 107.55883 .X -194.39988

dmx= -18.80000 X+ 107.55883

dx

X =107.55883

18.80000


Dx = RHI - ( q.X )

= 107.55883 - ( 18.80000 X )

X 0 1 2 3 4 5

Dx 107.55883 88.75883 69.95883 51.15883 32.35883 13.55883

Interval : ( 5 ≤ X ≤ 10 )

Mx =

= 107.55883 . X - 0.5 18.8 . X² - 194.39988 - 18.80000 X + 94.00000

= -9.40000 . X² + 88.75883 . X -100.39988

X 5 6 7 8 9 10

Mx 108.39428 93.75311 60.31194 8.07078 -62.97039 -152.81156


Mx = -9.40000 . X² + 88.75883 .X -100.39988

a = -9.40000

b = 88.75883

c = -100.39988

X =-b ± b² - 4ac

2a

X =-88.75883 ± 88.75883 2 - 4 -9.40000 . -100.39988

2 -9.40000

X =-88.75883 ± 64.05540

-18.80000

=-88.75883 + 64.05540

X1

X2

RHI.X - 1/2.q.X2 - MHI - P ( x-5 )

X1

=-18.80000

= 1.31401

=-88.75883 -64.05540

-18.80000

= 8.12842

Mx = 0

M ( 1.31401 ) = -9.40000 .( 1.31401 2 )+( 88.75883 1.31401 ) -100.39988

= 0.00000 …..OK!!!!

Mmax = -9.40000 . X² + 88.75883 .X -100.39988

dmx= -18.80000 X+ 88.75883

dx

X =88.75883

18.80000

= 4.72121

Mmax = -9.40000 .( 4.72121 2 )+( 88.75883 4.72121 ) -100.39988

= 109.12486 tm

Dx = RHI - ( q.X ) - P

= 107.55883 - ( 18.80000 X ) - 18.80000

= 88.75883 - ( 18.80000 X )

X 5 6 7 8 9 10

Dx -5.24117 -24.04117 -42.84117 -61.64117 -80.44117 -99.24117

² BATANG AD

D HAD

48.41593

4.00

X

29.0739236 HAD

» Reaksi A

∑ MD = 0

HAD . L + MAD + MDA = 0.0000

HAD . 4 + 29.07392 + 48.41593 = 0.00000

4 HAD + 77.48985 = 0.00000

HAD = -19.37246 ton …..→∑ H = 0

HAD - HDA = 0.00000

-19.37246 - HDA = 0.00000

HDA = 19.37246 ton …..←» Bidang M dan D

Interval : ( 0 ≤ X ≤ 4 )

X1

X2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

1/2

Mx = MAD +HAD.X

= 29.07392 -19.37246 X

X 0 1 2 3 4

Mx 29.07392 9.70146 -9.67100 -29.04347 -48.41593

Titik balik M = 29.07392 -19.37246 X

x = -1.50079 m

Dx = HAD

= -19.37246

X 0 1 2 3 4

Dx -19.37246 -19.37246 -19.37246 -19.37246 -19.37246

² BATANG BE

E HEB

4.80256

4.00

X

2.46468 HBE

» Reaksi B

∑ ME = 0

HBE . L + MBE - MEB = 0.0000

HBE . 4 + 2.46468 - 4.80256 = 0.00000

4 HBE + -2.33789 = 0.00000

HBE = 0.58447 ton …..←∑ H = 0

HBE - HEB = 0.00000

0.5845 - HEB = 0.00000

HEB = -0.58447 ton …..→

» Bidang M dan D

Interval : ( 0 ≤ X ≤ 4 )

Mx = MBE +HBE.X

= 2.46468 + 0.58447 X

X 0 1 2 3 4

Mx 2.46468 3.04915 3.63362 4.21809 4.80256

Titik balik M = ----(NO)

Dx = HBE

= 0.58447

X 0 1 2 3 4

Dx 0.58447 0.58447 0.58447 0.58447 0.58447

1/2

² BATANG CF

F HFC

53.3452841

4.00

X

21.80668 HCF

C

» Reaksi

∑ MF = 0

HCF . L - MCF - MFC = 0.0000

HCF . 4 -21.80668 -53.34528 = 0.00000

4 HCF -75.15197 = 0.00000

HCF = 18.78799 ton …..←∑ H = 0

HCF - HFC = 0.00000

18.7880 - HFC = 0.00000

HFC = -18.78799 ton …..→

» Bidang M dan D

Interval : ( 0 ≤ X ≤ 4 )

Mx = MCF -HCF.X

= 21.80668 ( 18.78799 X )

X 0 1 2 3 4

Mx 21.80668 40.59468 59.38267 78.17066 96.95865

Titik balik M = 21.80668 ( 18.78799 X )

x = -1.16067

Dx = HCF

= 18.7880

X 0 1 2 3 4

Dx 18.78799 18.78799 18.78799 18.78799 18.78799

1/2

² BATANG DG

G HGD

155.9463227

4.00

X

113.81135 HDG

D

» Reaksi

∑ MG = 0

HDG . L + MDG + MGD = 0.0000

HDG . 4 + 113.81135 + 155.94632 = 0.00000

4 HDG + 269.75768 = 0.00000

HDG = -67.43942 ton …..→∑ H = 0

HDG - HGD = 0.00000

-67.4394 - HGD = 0.00000

HGD = 67.43942 ton …..←» Bidang M dan D

Interval : ( 0 ≤ X ≤ 4 )

Mx = MDG -HDG.X

= 113.81135 ( -67.43942 X )

X 0 1 2 3 4

Mx 113.81135 46.37194 -21.06748 -88.50690 -155.94632

Titik balik M = 113.81135 ( -67.43942 X )

x = 1.68761

Dx = HDG

= -67.43942

X 0 1 2 3 4

Dx -67.43942 -67.43942 -67.43942 -67.43942 -67.43942

² BATANG EH

H HHE

2.67870

4.00

X

1/2

2.73633 HEH

E

» Reaksi

∑ MH = 0

HEH . L - MEH + MHE = 0.0000

HEH . 4 -2.73633 + 2.67870 = 0.00000

4 HEH -0.05763 = 0.00000

HEH = 0.01441 ton …..←∑ H = 0

HEH - HHE = 0.00000

0.01441 - HHE = 0.00000

HHE = -0.01441 ton …..→» Bidang M dan D

Interval : ( 0 ≤ X ≤ 4 )

Mx = -MEH + HEH.X

= -2.73633 + ( 0.01441 X )

X 0 1 2 3 4

Mx -2.73633 -2.72192 -2.70751 -2.69311 -2.67870

Titik balik M = ----(NO)

Dx = HEH

= 0.01441

X 0 1 2 3 4

Dx 0.01441 0.01441 0.01441 0.01441 0.01441

² BATANG IF

I HIF

152.811556

4.00

X

116.88850 HFI

F

» Reaksi

∑ MH = 0

HFI . L - MFI - MIF = 0.00000

HFI . 4 -116.88850 -152.81156 = 0.00000

1/2

4 HFI + -269.70005 = 0.00000

HFI = 67.42501 ton …..←∑ H = 0

HFI - HIF = 0.00000

67.42501 - HIF = 0.00000

HIF = -67.42501 ton …..→» Bidang M dan D

Interval : ( 0 ≤ X ≤ 4 )

Mx = -MFI+HFI.X

= -116.88850 + ( 67.42501 X )

X 0 1 2 3 4

Mx -116.88850 -49.46348 17.96153 85.38654 152.81156

Titik balik M = -116.88850 + 67.42501 X

x = 1.73361

Dx = HFI

= 67.42501

X 0 1 2 3 4

Dx 67.42501 67.42501 67.42501 67.42501 67.42501

E. PERHITUNGAN GAYA NORMAL

AD = - RGH - RDE

= -99.82251 -97.33631

= -197.15883 ton

DE = + HDG - HDA

= 67.43942 -19.37246

= 48.06696 ton

DG = - RGH

= -99.82251 ton

GH = - HGD

= -67.43942 ton

HI = - HGD + HHE

= -67.43942 + 0.01441

= -67.42501 ton

EF = + HDG - HDA - HEH + HEB

1/2

= 67.43942 -19.37246 -0.01441 + 0.58447

= 48.63702 ton

EH = - RHI - RHG

= -107.55883 -106.97749

= -214.53632 ton

FI = - RIH

= -99.24117 ton

BE = - RHG - RHI - RED - REF

= -106.97749 -107.55883 -109.46369 -100.38915

= -424.38915 ton

CF = - RIH - RFE

= -99.24117 -106.41085

= -205.65202 ton

mektek iv

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